Question: Solve for $x$ and $y$ using elimination. ${-4x-5y = -44}$ ${x+2y = 17}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${-4x-5y = -44}$ $4x+8y = 68$ Add the top and bottom equations together. $3y = 24$ $\dfrac{3y}{{3}} = \dfrac{24}{{3}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-4x-5y = -44}\thinspace$ to find $x$ ${-4x - 5}{(8)}{= -44}$ $-4x-40 = -44$ $-4x-40{+40} = -44{+40}$ $-4x = -4$ $\dfrac{-4x}{{-4}} = \dfrac{-4}{{-4}}$ ${x = 1}$ You can also plug ${y = 8}$ into $\thinspace {x+2y = 17}\thinspace$ and get the same answer for $x$ : ${x + 2}{(8)}{= 17}$ ${x = 1}$